[Resource Topic] 2024/798: Incompressible Functional Encryption

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Incompressible Functional Encryption

Authors: Rishab Goyal, Venkata Koppula, Mahesh Sreekumar Rajasree, Aman Verma


Incompressible encryption (Dziembowski, Crypto’06; Guan, Wichs, Zhandry, Eurocrypt’22) protects from attackers that learn the entire decryption key, but cannot store the full ciphertext. In incompressible encryption, the attacker must try to compress a ciphertext within pre-specified memory bound S before receiving the secret key.

In this work, we generalize the notion of incompressibility to functional encryption. In incompressible functional encryption, the adversary can corrupt non-distinguishing keys at any point, but receives the distinguishing keys only after compressing the ciphertext to within S bits. An important efficiency measure for incompressible encryption is the ciphertext-rate ( i.e., \mathsf{rate} = \frac{|m|}{|\mathsf{ct}|}\;). We give many new results for incompressible functional encryption:

  1. Incompressible attribute-based encryption for circuits from standard assumptions, with \mathsf{ct}-rate-\frac{1}{2} and short secret keys,
  2. Incompressible functional encryption for circuits from (non-incompressible) functional encryption, with
    (a) \mathsf{ct}-rate-\frac{1}{2} and short secret keys,
    (b) \mathsf{ct}-rate-1 and large secret keys.

Our results achieve optimal efficiency, as incompressible attribute-based/functional encryption with \mathsf{ct}-rate-1 as well as short secret keys has strong implausibility barriers. Moreover, our assumptions are minimal as incompressible attribute-based/functional encryption are strictly stronger than their non-incompressible counterparts.

ePrint: https://eprint.iacr.org/2024/798

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